Statistical structure of turbulent-boundarylayer velocity-vorticity products at high and low Reynolds numbers

The mean wall-normal gradients of the Reynolds shear stress and the turbulent kinetic energy have direct connections to the transport mechanisms of turbulent-boundary-layer flow. According to the Stokes-Helmholtz decomposition, these gradients can be expressed in terms of velocity-vorticity products. Physical experiments were conducted to explore the statistical properties of some of the relevant velocity-vorticity products. The high-Reynolds-number data (R-theta similar or equal to O(10(6)), where theta is the momentum thickness) were acquired in the near neutrally stable atmospheric-surface-layer flow over a salt playa under both smooth- and rough-wall conditions. The low-R-theta data were from a database acquired in a large-scale laboratory facility at 1000 < R-theta < 5000. Corresponding to a companion study of the Reynolds stresses (Priyadarshana & Klewicki, Phys. Fluids, vol. 16, 2004, p. 4586), comparisons of low- and high-R-theta as well as smooth- and rough-wall boundary-layer results were made at the approximate wall-normal locations y(p)/2 and 2y(p), where y(p) is the wall-normal location of the peak of the Reynolds shear stress, at each Reynolds number. In this paper, the properties of the v omega(z), omega omega(y) and u omega(z) products are analysed through their statistics and cospectra over a three-decade variation in Reynolds number. Here u, v and w are the fluctuating streamwise, wall-normal and spanwise velocity components and omega(y) and omega(y) are the fluctuating wall-normal and spanwise vorticity components. It is observed that v-omega(z) statistics and spectral behaviours exhibit considerable sensitivity to Reynolds number as well as to wall roughness. More broadly, the correlations between the v and omega fields are seen to arise from a 'scale selection' near the peak in the associated vorticity spectra and, in some cases, near the peak in the associated velocity spectra as well.